PACF cuts off at lag 2, ACF tails off

Question

For a stationary series, the sample ACF tails off gradually (a damped, decaying pattern). The sample PACF is significant at lags 1 and 2, then drops inside the bands for lag 3 onward. Which model does this pattern indicate?

Accepted Answer

Use the rules: - AR(p): ACF tails off, PACF cuts off after lag p. - MA(q): ACF cuts off after lag q, PACF tails off. Here the ACF tails off and the PACF cuts off after lag 2, so p = 2 and the model is AR(2). The PACF at lag k measures the direct association between Xt and X{t-k} after removing everything explained by the intervening lags. For an AR(2), the current value depends directly on the previous two values and nothing further back, so the PACF has meaningful spikes at lags 1 and 2 and then vanishes. The ACF, meanwhile, decays gradually (sometimes with an oscillating or damped-wave shap…

PACF cuts off at lag 2, ACF tails off

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